22 Questions
What is the primary goal of the greedy decision tree learning algorithm?
To select the best feature to split the data
What is the problem of selecting the best feature to split the data referred to as?
Problem 1: Feature Selection
How is the classification error calculated in a decision tree?
By calculating the proportion of misclassified instances
What is the purpose of calculating the entropy in a decision tree?
To measure the impurity of the data
What is the stopping condition in a decision tree?
When no more splits improve the accuracy
What is the main difference between the greedy decision tree learning algorithm and other decision tree algorithms?
The greedy algorithm selects the best feature to split the data at each node
What is the problem of determining when to stop splitting the data referred to as?
Problem 2: Stopping Condition
What is the entropy when all examples are of the same class?
0
What is the purpose of calculating the information gain in a decision tree?
To measure the effectiveness of a split
What is the formula for calculating entropy?
∑ - pi log2 pi
What is the information gain in the context of decision trees?
Entropy of the parent minus the weighted average entropy of the children
What is the purpose of the feature split selection algorithm?
To select the feature with the highest information gain
What is the entropy of the example 'ssss'?
0
What is the information gain when splitting on the 'Credit' feature?
0.6599
Why is the decision split on the 'Credit' feature?
Because it has the highest information gain
What is the entropy of the example 'sf'?
1
What is the primary objective when choosing feature h*(x) in decision tree learning?
Lowest classification error
What is the next step after learning a decision stump?
Recursive stump learning
What is the first stopping condition in decision tree learning?
All data agrees on y
What is the main characteristic of greedy decision tree learning?
It selects the best feature at each step
What is the final output of the decision tree prediction algorithm?
A predicted class label
What is the main idea behind tree learning?
Recursive stump learning
Study Notes
Decision Trees
- Step-by-step process for greedy decision tree learning:
- Start with an empty tree
- Select a feature to split data
- For each split of the tree, determine whether to make predictions or continue splitting
- Feature selection criteria:
- Entropy and Information Gain
Entropy and Information Gain
- Entropy: measures the impurity of data
- If all examples are of the same class, entropy = 0
- If examples are evenly split between classes, entropy = 1
- Formula: 𝐸𝑛𝑡𝑟𝑜𝑝𝑦 = ∑ - 𝑝𝑖 log 2 𝑝𝑖
- Information Gain: measures the effectiveness of a split
- Formula: Information Gain = Entropy (parent) - (weighted average) Entropy (children)
Calculating Information Gain
- Example 1: Credit feature
- Entropy (parent) = 0.9905
- Entropy (excellent) = 0
- Entropy (fair) = 0.8865
- Entropy (poor) = 0.769
- Information Gain = 0.9905 - (0.225)(0) - (0.325)(0.8865) - (0.45)(0.769) = 0.6599
- Example 2: Term feature
- Entropy (3 years) = 0.72
- Entropy (5 years) = 0.88
- Information Gain = 0.9905 - (0.5)(0.72) - (0.5)(0.88) = 0.1905
- Decision: Split on Credit feature since it has the highest Information Gain (0.6599)
Feature Split Selection Algorithm
- Given a subset of data M (a node in a tree)
- For each feature hi(x):
- Split data of M according to feature hi(x)
- Compute classification error OR Information gain split
- Choose feature h*(x) with lowest classification error or highest Information gain
Recursion and Stopping Conditions
- Tree learning = Recursive stump learning
- Stopping conditions:
- All data agrees on y
- Already split on all features
Prediction Algorithm
- Decision tree prediction algorithm
- Greedy decision tree learning
This lecture covers decision trees, feature selection criteria, entropy, and information gain in pattern recognition. Instructor Dr. Dina Khattab teaches this course at Ain Shams University.
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